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        <section id="main"><article id="post-（强行算法）对2019点美赛D题极端化的算法探讨、设计与遇到的问题（未完,但可能也到此为止）" class="wow slideInRight article article-type-post" itemscope itemprop="blogPost">
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      （强行算法）对2019点美赛D题极端化的算法探讨、设计与遇到的问题（未完,但可能也到此为止）.md
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        <h2 id="说明-2022-05-05"><a class="markdownIt-Anchor" href="#说明-2022-05-05"></a> 说明 - 2022-05-05</h2>
<p>本篇博客为本人原创, 原发布于CSDN, 在搭建个人博客后使用爬虫批量爬取并挂到个人博客, 出于一些技术原因博客未能完全还原到初始版本(而且我懒得修改), 在观看体验上会有一些瑕疵 ,若有需求会发布重制版总结性新博客。发布时间统一定为1111年11月11日。钦此。</p>
<h4 id="卢浮宫-某建筑疏散问题-时序无向图"><a class="markdownIt-Anchor" href="#卢浮宫-某建筑疏散问题-时序无向图"></a> <s>卢浮宫</s> 某建筑疏散问题 <s>时序无向图？</s></h4>
<p>不考虑残疾人，不考虑工作人员，不考虑一切麻烦事。只考虑一群正常人走出建筑，怎样最快。<br />
核心思路是随着时间的增加不断扩大每个出口的覆盖范围，让出口在覆盖范围内“找人”代表路线的规划</p>
<h4 id="0-铺垫定义"><a class="markdownIt-Anchor" href="#0-铺垫定义"></a> 0. 铺垫定义</h4>
<p>假设某建筑有好几层，层与层之间有若干通道连接，将这些通道定义为 <strong>窄道</strong> （如楼梯），出口有若干个，可以存在于任意一层，出口与外界之间也存在<br />
<strong>窄道</strong> （如门）（若人是源源不断的，则通过门和通过楼梯所需的平均时间近似相等）</p>
<h4 id="1定义-单位时间"><a class="markdownIt-Anchor" href="#1定义-单位时间"></a> 1.定义 单位时间</h4>
<p>选一个合适的时间长度当 <strong>单位时间</strong></p>
<h4 id="2定义-单位距离"><a class="markdownIt-Anchor" href="#2定义-单位距离"></a> 2.定义 单位距离</h4>
<p><strong>单位时间</strong> 内人按某个速度匀速行进的距离作为 <strong>单位距离</strong> （eg：走楼梯和走平地在 <strong>单位时间</strong> 内走过的距离可能不同，但他们同为<br />
<strong>单位距离</strong> ，即只算时间），单位时间内能通过 <strong>窄道</strong> 的最大人数称为该出口的 <strong>最大流量</strong></p>
<h4 id="3定义-宽道-窄道"><a class="markdownIt-Anchor" href="#3定义-宽道-窄道"></a> 3.定义 宽道 窄道</h4>
<p>把建筑划分成若干个大小基本相等的多边形（或椭圆形）区域称为 <strong>节点</strong><br />
（对应图数据结构中的点）。相邻的点之间存在通道（对应图数据结构中的边）（大厅或长廊中从一个点到另一个点、连接两个点的楼梯都是通道），若一个通道不是<br />
<strong>窄道</strong> ，则将其定义为 <strong>宽道</strong> ，所有的通道的长度都要求近似符合 <strong>单位距离</strong> 。<br />
默认 <strong>窄道</strong> 人多时会发生拥挤，人流速度受限制，而 <strong>宽道</strong> 不会发生拥挤，人流速度为“无限大”（ <strong>宽道</strong> 可以拥挤，但其拥挤的原因是<br />
<strong>窄道</strong> 限速，所以认为 <strong>宽道</strong> 不拥挤）</p>
<h4 id="4算法思路定义"><a class="markdownIt-Anchor" href="#4算法思路定义"></a> 4.算法思路+定义</h4>
<p>找到所有的出口，刚开始它们的 <strong>时间计数</strong> 为0。<br />
时间计数决定了出口的覆盖范围。（eg：当 <strong>时间计数</strong> 为0时，只有在出口区域一部分人可以逃离建筑；当 <strong>时间计数</strong> 为5时，距离任意一个出口五个<br />
<strong>单位距离</strong> 的人都可以理论上逃离建筑–无视碰撞体积的情况）</p>
<h4 id="5算法思路"><a class="markdownIt-Anchor" href="#5算法思路"></a> 5.算法思路</h4>
<p><strong>循环：</strong><br />
{<br />
1.出口的人数 减少 <strong>最大流量</strong> ，但不能低于0<br />
2. <strong>时间计数</strong> +1<br />
3.若距离出口附近的人数&lt;出口 <strong>最大流量</strong> ：出口点可以在距离自己 <strong>时间计数</strong> 个 <strong>单位距离</strong> 的范围内找人补充人数至 <strong>最大流量</strong><br />
。<br />
注：*递归： * 当出口的覆盖范围中包含 <strong>窄道</strong> 时，应优先从窄道另一端的点找人， <strong>见考虑1</strong> ，进行递归。（若 <strong>窄道</strong><br />
另一端覆盖的范围内存在新的窄道，则这一寻找中优先考虑新的窄道）<br />
}<br />
<strong>终止条件:</strong> <s>所有的点全部覆盖 <strong>且</strong></s> 所有人都逃出生天</p>
<h4 id="a考虑1"><a class="markdownIt-Anchor" href="#a考虑1"></a> a.考虑1</h4>
<p><strong>为什么窄道另一端优先</strong><br />
eg：2层楼疏散，只有一楼有出口，1、2层之间存在若干窄道，出口与外界之间存在若干窄道。姑且把前者称为 <strong>远级窄道</strong> ，后者称为 <strong>近级窄道</strong> 。<br />
显然疏散的最快速度时取决于 <strong>近级窄道</strong> 的。若不给 <strong>远级窄道</strong> 较高的优先级，而恰好所有的 <strong>远级窄道</strong> 的最大流量和&lt;所有<br />
<strong>近级窄道</strong> 的最大流量和，就很可能会出现1楼的人已经疏散完，留下大量的出口，而2楼的人无法及时下来的情况。</p>
<p>这只是一种找到每个通道需要走多少人的办法。当走一条通道的总人数固定，哪里的人先走对时间几乎没有影响。</p>
<h4 id="a问题1"><a class="markdownIt-Anchor" href="#a问题1"></a> A.问题1</h4>
<p>同时涵盖到多条窄道时，如何抉择？(好像遇到坑了，怎么感觉需要花式DP啊）</p>
<h4 id="代码数组模拟数据结构未完成"><a class="markdownIt-Anchor" href="#代码数组模拟数据结构未完成"></a> 代码（数组模拟数据结构）（未完成）</h4>
<p>​</p>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;iostream&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;cstdio&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;cstring&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;cstdlib&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;cmath&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;queue&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;map&gt;</span></span></span><br><span class="line"><span class="keyword">typedef</span> <span class="type">long</span> <span class="type">long</span> ll;</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="type">const</span> INF = <span class="number">1e7</span>+<span class="number">7</span>;</span><br><span class="line"><span class="type">int</span> <span class="type">const</span> maxf = <span class="number">10</span>;  <span class="comment">//最大楼层数</span></span><br><span class="line"><span class="type">int</span> <span class="type">const</span> maxn = <span class="number">20</span>;  <span class="comment">//楼层出口最大数目</span></span><br><span class="line"><span class="type">int</span> <span class="type">const</span> maxd = <span class="number">40</span>;  <span class="comment">//区域距离最远楼层出口的最大距离+1</span></span><br><span class="line"><span class="type">int</span> <span class="type">const</span> maxv = <span class="number">1000</span>;<span class="comment">//最多节点个数</span></span><br><span class="line"></span><br><span class="line"><span class="type">int</span> inode,iedge,cntout;</span><br></pre></td></tr></table></figure>
<p>​</p>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">struct</span> <span class="title class_">Node</span></span><br><span class="line">&#123;</span><br><span class="line">    <span class="type">int</span> num;        <span class="comment">//此节点的人数</span></span><br><span class="line">    <span class="type">int</span> dis[maxn];  <span class="comment">//此节点距离楼层中每个出口的距离</span></span><br><span class="line">    Node *nxt[maxn];<span class="comment">//指向跟这个节点与出口i距离相同的下一个节点</span></span><br><span class="line">    <span class="type">bool</span> narrow;   <span class="comment">//这个节点是否是窄道的入点、出点</span></span><br><span class="line">    Node *special;  <span class="comment">//窄道另一端的点 仅在isIN或isOUT为true时生效</span></span><br><span class="line">&#125;node[maxv];</span><br><span class="line"></span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">Edge</span></span><br><span class="line">&#123;</span><br><span class="line">    <span class="type">int</span> to,speed;   <span class="comment">//通道速度 单位时间内能通过通道的最大人数 宽道默认很大</span></span><br><span class="line">    <span class="type">bool</span> narrow;    <span class="comment">//是否为窄道</span></span><br><span class="line">&#125;edge[maxv&lt;&lt;<span class="number">3</span>];</span><br><span class="line"></span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">FLOOR</span></span><br><span class="line">&#123;</span><br><span class="line">    <span class="type">int</span> exitNum;        <span class="comment">//出口数目</span></span><br><span class="line">    <span class="type">int</span> nodeNum;        <span class="comment">//这层楼的节点总数</span></span><br><span class="line">    <span class="type">int</span> zero;           <span class="comment">//无人节点数</span></span><br><span class="line">    <span class="type">bool</span> isempty;       <span class="comment">//楼层是否为空</span></span><br><span class="line">    Node *Dnode[maxn][maxd] <span class="comment">//与第i个出口距离为j的节点组成的链表的头节点指针</span></span><br><span class="line">&#125;floor[maxf];</span><br></pre></td></tr></table></figure>
<p>​</p>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">void</span> <span class="title">init</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    inode = iedge = cntout = <span class="number">-1</span>;</span><br><span class="line">    <span class="built_in">memset</span>(head,<span class="number">-1</span>,<span class="built_in">sizeof</span>(head));</span><br><span class="line"></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<p>​</p>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<p>​<br />
​</p>
<h4 id="题目描述"><a class="markdownIt-Anchor" href="#题目描述"></a> 题目描述</h4>
<p><strong>2019 ICM<br />
Problem D: Time to leave the Louvre</strong><br />
The increasing number of terror attacks in France[1]<br />
requires a review of the emergency<br />
evacuation plans at many popular destinations. Your ICM team is helping to<br />
design evacuation<br />
plans at the Louvre in Paris, France. In general, the goal of evacuation is to<br />
have all occupants<br />
leave the building as quickly and safely as possible. Upon notification of a<br />
required evacuation,<br />
individuals egress to and through an optimal exit in order to empty the<br />
building as quickly as<br />
possible.<br />
The Louvre is one of the world’s largest and most visited art museum,<br />
receiving more than 8.1<br />
million visitors in 2017[2]<br />
. The number of guests in the museum varies throughout the day and<br />
year, which provides challenges in planning for regular movement within the<br />
museum. The<br />
diversity of visitors – speaking a variety of languages, groups traveling<br />
together, and disabled<br />
visitors – makes evacuation in an emergency even more challenging.<br />
The Louvre has five floors, two of which are underground.<br />
![在这里插入图片描述](<a target="_blank" rel="noopener" href="https://img-blog.csdnimg.cn/20210112235110425.png?x-oss-">https://img-blog.csdnimg.cn/20210112235110425.png?x-oss-</a><br />
process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dsZGNtenk=,size_16,color_FFFFFF,t_70#pic_center)<br />
The 380,000 exhibits located on these five floors cover approximately 72,735<br />
square meters,<br />
with building wings as long as 480 meters or 5 city blocks[3]. The pyramid<br />
entrance is the main<br />
and most used public entrance to the museum. However, there are also three<br />
other entrances<br />
usually reserved for groups and individuals with museum memberships: the<br />
Passage Richelieu<br />
entrance, the Carrousel du Louvre entrance, and the Portes Des Lions entrance.<br />
The Louvre has<br />
an online application, “Affluences” (<a target="_blank" rel="noopener" href="https://www.affluences.com/louvre.php">https://www.affluences.com/louvre.php</a>),<br />
that provides realtime updates on the estimated waiting time at each of these<br />
entrances to help facilitate entry to<br />
the museum. Your team might consider how technology, to include apps such as<br />
Affluences, or<br />
others could be used to facilitate your evacuation plan.<br />
Only emergency personnel and museum officials know the actual number of total<br />
available exit<br />
points (service doors, employee entrances, VIP entrances, emergency exits, and<br />
old secret<br />
entrances built by the monarchy, etc.). While public awareness of these exit<br />
points could provide<br />
additional strength to an evacuation plan, their use would simultaneously<br />
cause security concerns<br />
due to the lower or limited security postures at these exits compared with<br />
level of security at the<br />
four main entrances. Thus, when creating your model, your team should consider<br />
carefully when<br />
and how any additional exits might be utilized.<br />
Your supervisor wants your ICM team to develop an emergency evacuation model<br />
that allows<br />
the museum leaders to explore a range of options to evacuate visitors from the<br />
museum, while<br />
also allowing emergency personnel to enter the building as quickly as<br />
possible. It is important to<br />
identify potential bottlenecks that may limit movement towards the exits. The<br />
museum<br />
emergency planners are especially interested in an adaptable model that can be<br />
designed to<br />
address a broad set of considerations and various types of potential threats.<br />
Each threat has the<br />
potential to alter or remove segments of possible routes to safety that may be<br />
essential in a single<br />
optimized route. Once developed, validate your model(s) and discuss how the<br />
Louvre would<br />
implement it.<br />
Based on the results of your work, propose policy and procedural<br />
recommendations for<br />
emergency management of the Louvre. Include any applicable crowd management<br />
and control<br />
procedures that your team believes are necessary for the safety of the<br />
visitors. Additionally,<br />
discuss how you could adapt and implement your model(s) for other large,<br />
crowded structures.<br />
Your submission should consist of:<br />
 One-page Summary Sheet,<br />
 Your solution of no more than 20 pages, for a maximum of 21 pages with your<br />
summary.<br />
 Judges expect a complete list of references with in-text citations, but may<br />
not consider<br />
appendices in the judging process.<br />
 Note: Reference list and any appendices do not count toward the 21-page<br />
limit and<br />
should appear after your completed solution.<br />
References:<br />
[1] Reporters, Telegraph. “Terror Attacks in France: From Toulouse to the<br />
Louvre.” The<br />
Telegraph, Telegraph Media Group, 24 June 2018,<br />
<a target="_blank" rel="noopener" href="http://www.telegraph.co.uk/news/0/terrorattacks-france-toulouse-louvre/">www.telegraph.co.uk/news/0/terrorattacks-france-toulouse-louvre/</a>. [2] “8.1<br />
Million Visitors to the Louvre in 2017.” Louvre Press Release, 25 Jan. 2018,<br />
<a target="_blank" rel="noopener" href="http://presse.louvre.fr/8-1-million-visitors-to-the-louvre-in-2017/">presse.louvre.fr/8-1-million-visitors-to-the-louvre-in-2017/</a>. [3] “Interactive<br />
Floor Plans.” Louvre - Interactive Floor Plans | Louvre Museum | Paris,<br />
30 June 2016, <a target="_blank" rel="noopener" href="http://www.louvre.fr/en/plan">www.louvre.fr/en/plan</a>.<br />
[4] “Pyramid” Project Launch – The Musée du Louvre is improving visitor<br />
reception<br />
(2014-2016).” Louvre Press Kit, 18 Sept. 2014,<br />
<a target="_blank" rel="noopener" href="http://www.louvre.fr/sites/default/files/dp_pyramide%2028102014_en.pdf">www.louvre.fr/sites/default/files/dp_pyramide 28102014_en.pdf</a>.<br />
[5] “The ‘Pyramid’ Project - Improving Visitor Reception (2014-2016).” Louvre<br />
Press<br />
Release, 6 July 2016, <a target="_blank" rel="noopener" href="http://presse.louvre.fr/the-pyramid-project/">presse.louvre.fr/the-pyramid-project/</a>.<br />
Glossary:<br />
Bottlenecks – places where movement is dramatically slowed or even stopped.<br />
Emergency personnel – people who help in an emergency, such as guards, fire<br />
fighters,<br />
medics, ambulance crews, doctors, and police.</p>

      
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